There are a variety of uses of capacitance measuring devices. One use in particular relates to detection of material levels (such as, for example, fluid in a tank). In these applications, a capacitance measuring probe is disposed in a material-containing vessel. The vessel and the probe are at different potentials so as to form a capacitor therebetween. The air and material contained in the vessel act as dielectrics. As the material level changes, so does the capacitance between the probe and the vessel.
Capacitance is normally measured using one of the following parameters: (a) differential impedance or admittance; (b) phase difference; or (c) frequency (or time), based on capacitive reactance.
The differential impedance technique is based on the generalized impedance formula: ##EQU1## To use this technique, two parallel systems are established, each having identical drive frequency, drive amplitude, resistance and inductance. One system includes a reference capacitor of known value. The other system contains the capacitor which is to be measured. Thus, the only difference between the systems is capacitance. The output of the system with the known reference capacitor is compared to the output of the system with the unknown capacitance to determine a voltage or current differential. In accordance with Ohm's Law (v=iZ), the voltage (or current) differential is proportional to the values of capacitance.
One drawback to this system is that exact control and matching of inductances is difficult. Therefore, systems based on this principle, while very rugged, tend to have moderate overall accuracies (i.e., an error of approximately between one and three percent).
The phase difference technique is based on the capacitive reactance formula: ##EQU2## To use this technique, two parallel systems are established, each with identical drive frequency and drive phase. One system includes a reference capacitor of known value. The other system contains the capacitor which is to be measured. Thus, the only difference between the systems is capacitance. The different capacitance causes the system's outputs to have different phase angles. The difference of phase angles is theoretically proportional to the values of capacitance. Unfortunately, a phase system with a linear relationship between capacitance and phase angle can be realized only with difficulty, and overall accuracy tends to be poor.
The frequency and time-based techniques are based on the generalized extension of Maxwell's electromagnetic theory: EQU v=.lambda.f
Under this equation, frequency of repetitive waveforms is the inverse of wavelength (because velocity remains constant for a given set of propagation conditions). For a given time constant, EQU .tau.=RC,
the voltage Vc across a capacitor that is subjected to a charging voltage V is: ##EQU3## and the voltage across a discharging capacitor that is initially at voltage V is: ##EQU4## Reversing the charge and discharge equations allows substitution of current for voltage. The curves generated by the above equations are of exponential form and extend to asymptotes, never fully converging.
By establishing an electronic oscillator or multivibrator which uses capacitive reactance as the variable frequency-determining element, a proportionality is established between the value of the capacitor and the resultant frequency or wavelength. Integrated circuit astable and monostable circuits (such as the 555 timer) often use this principle, and have been used to measure capacitance.
Typical gating for these forms of measurement is some form of comparator. Since waveforms are either exponential or transcendental (i.e., constantly varying slope), fixed comparator propagation delays contribute to errors. Frequency based systems also suffer from nonsynchronous gating, resulting in a.+-.1 count errorband.
For use in (industrial) metrology systems, the symmetrical bipolar waveforms of sinusoidal oscillators are preferable. Typical pulse mode and astable type systems generate asymmetrically polarized waveforms which cause plating with certain chemical (i.e., ionic) dielectrics. Systems which A.C. couple (via a very large capacitor) to the sensed dielectric are also common. These charges are never totally in balance, resulting in plating.
Since frequency is directly proportional to capacitive reactance and inversely proportional to capacitance, a direct reading instrument based on frequency tends to be complex (usually requiring digital division). Time based systems are relatively simple due to direct scaling proportionality.